Bispinor auxiliary fields in duality-invariant electrodynamics revisited

Motivated by recent progress in studying the duality-symmetric models of nonlinear electrodynamics, we revert to the auxiliary tensorial (bispinor) field formulation of the O (2) duality proposed by us in Ivanov and Zupnik Nucl. Phys. B618, 3 (2001) ; Yad. Fiz. 67, 2212 (2004). In this approach, the entire information about the given duality-symmetric system is encoded in the O (2) -invariant interaction Lagrangian which is a function of the auxiliary fields V_, V { }. We extend this setting to duality-symmetric systems with higher derivatives and show that the recently employed ``nonlinear twisted self-duality constraints'' amount to the equations of motion for the auxiliary tensorial fields in our approach. Some other related issues are briefly discussed and a few instructive examples are explicitly worked out.